Deeper than primes

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DazzaD said:
And can I point out to Doron that

pi is not contingent upon "circumference/diameter", it has a clearly defined value in mathematics regardless of this application in geometry (something he may want to consider when invoking the Koch-type diagrams)..

and that A Level maths students in the UK (ages 16-18) are well versed in the "sum to infinity of a geometric series" and would struggle greatly to understand one line of his explanation about why that series does NOT 'have' a finite sum.
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A local number like Pi has a strict location along a given 1-dim space.

A non-local number like 3.14...[base 10] does not have a strict location along a given 1-dim space.


More about non-local numbers can be found in http://www.scribd.com/doc/16542245/OMPT page 11.
 
The Man said:
You can notate you notions by any means that suit you, though please let us know when you can acctualy notate any self-consistency, general consistency or practical application (like an ‘infinite interpolation energy’ toaster) of your notions.
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n = 1 to ∞

Saying it over and over doesn't make it true, The Man. The fact remains that in real Mathematics points are not completely cover a line, simply because no amount of 0 to n-1 dimensional spaces is n dimensional space ad infinitum ... exactly because any given dimensional space is not a collection of the previous dimensional spaces.

The irreducibility of a given dimensional space > 0 to the previous dimensional spaces is exactly the considered energy, and it clealy seen by cases like http://arxiv.org/PS_cache/arxiv/pdf/0910/0910.2709v1.pdf .
 
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In addition to post http://www.internationalskeptics.com/forums/showpost.php?p=6419092&postcount=11922 , you are invited to look at Dr. Reva Kay Williams' work (University of Florida) which developed a rigorous proof that validated Penrose's mechanism ( http://en.wikipedia.org/wiki/Gravitomagnetism#cite_note-2 ).

Here is a paper of her ( http://arxiv.org/PS_cache/astro-ph/pdf/0210/0210139v4.pdf ) with the title "NEW ENERGY SOURCE CONTROLLED BY GRAVITY ALONE?" ( the published version is in http://iopscience.iop.org/0004-637X/611/2/952/ ).
 
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doronshadmi said:
What you call "a number of iterations" is equivalent to interpolation, which is strict if it is finite interpolation, or non-strict if it is infinite interpolation (in infinite interpolation, non-local numbers like 0.999…[base 10] and 0.000…1[base 10] are used).
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There is no equivalency -- only in your dreams. Interpolation solves the question of WHERE, whereas iterations solve the question of HOW MANY. Interpolation locates point on a curve where the actual point doesn't exist, coz the acquired data doesn't show its value, like in the statistical research. Interpolation is based on a function that describes the curve, whereas iteration is a n-step in the algorithm that generates geometric forms, such as fractals. The effect resembles interpolation. Some call the process where the number of iterated elements increases along a constant curve a "Fractal Interpolation" to distinguish from the cases where the curve is changing, such as in the case of the basic Koch form.

http://hypatia.math.uri.edu/~kulenm/honprsp02/interpolation.html

Here, the number of squares N appearing in the line segment of constant shape, length and direction is a function of iterations k: N = 2k where the initial shape is k=0.

The Mandelbrot set is generated quite differently; it appears on the complex plane, not in the Euclidean space.
 
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doronshadmi said:
The fact remains that in real Mathematics points are not completely cover a line, simply because no amount of 0 to n-1 dimensional spaces is n dimensional space ad infinitum ... exactly because any given dimensional space is not a collection of the previous dimensional spaces.
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There you go again repeating yourself. And yet, you are still wrong. Lines in real Mathematics continue to be completely covered by points.

doronshadmi said:
You are talking about the the complex form...<gibberish snipped>...
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No, I wasn't. I was talking about simple lines and that fact you cannot support your claim lines are not covered completely by points. You cannot support your claim because it is blatantly false, and your attempts to obscure things with your meaningless concatenation of glyphs doesn't alter that fundamental truth.
 
epix said:
Interpolation solves the question of WHERE, whereas iterations solve the question of HOW MANY.
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Interpolation is iterations within a given domain, where extrapolation is iterations out of a given domain.

In both cases we can ask "How many iterations there are?"

Finite amount of iterations have a strict value.

Infinite amount of iterations do not have a strict value.

epix said:
The Mandelbrot set is generated quite differently; it appears on the complex plane, not in the Euclidean space.
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It does not matter, because we still ask "How many iterations there are?"

--------

Let us correct some mistake about your understanding of OM.

0.999…[base 10]() on its own, is not a collection.

1() on its own, is not a collection.

1(0.999…[base 10]()) is a collection that does not change the fact that 1() existence is above 0.999…[base 10]() existence, where 1() and 0.999…[base 10]() are not defined by each other, for example:

∞(
0(),0.999…[base 10](),1(),2(),3(), …
)
 
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jsfisher said:
I was talking about simple lines and that fact you cannot support your claim lines are not covered completely by points.
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By traditional reasoning you are unable to define the fundamentals that enable collections.

No collection exists unless different levels of existence are considered.

For example:

0() on its own is not a collection.

1() on its own is not a collection.

2() on its own is not a collection.

…

etc. … ad infinitum.


On the contrary 1(0()) is a collection, but is does not change the fact that 1() and 0() are not defined by each other, or in other words, 1() is not a collection of any amount of 0() simply because 1() is a different level of existence, which is above the existence of 0().

In other words, no amount of 0() completely covers 1(), which is a level of existence above the existence of 0().

jsfisher, traditional reasoning can't get http://www.internationalskeptics.com/forums/showpost.php?p=6418915&postcount=11918 .
 
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jsfisher said:
There you go again repeating yourself. And yet, you are still wrong. Lines in real Mathematics continue to be completely covered by points.
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The problem is that Doron cannot come up with some function y = f(x) continuous in domain a ≤ x ≤ b and show that there is xp for which there is no corresponding yp. Instead, his argument involves strange symbolism that almost requires disk defragmentation when it shows up on your PC screen.

The second, related problem, and decidedly not the last, is that Doron cannot convert his ideas into the standard math language or near-standard and make the substitution "my stuff = their stuff." That's probably because Doron's ideas are so deep that they leave the standard math speechless. So he will continue to speak Doronese wondering what kind of dummies that evolution came up with.
 
doronshadmi said:
Interpolation is iterations within a given domain, where extrapolation is iterations out of a given domain.
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There is no fractal extrapolation, and if there is, show me one.

The Sierpinski Triangle is a collection of self-repeating triangles. You draw the initial shape that consists of three lines. Lines are made of points with dim=0. That means, they are all equal, as 0=0, and that's why you see what you see.
http://www.zeuscat.com/andrew/chaos/sierpinski.clear.gif

Inspired by the Mandelbrot set, the dimensionality of the points can be changed according to the number of iterations it requires to draw additional self repeating patters. Drawing lines also means drawing points, and that's why you see what you see.
http://curvebank.calstatela.edu/sierpinski/1deposit2sierp.gif

Unlike in the case of the first triangle, the algorithm for this triangle draws points, not lines.
 
doronshadmi said:
By using traditional reasoning you are inverted to demonstrate the case where x is both ≥ a, or x is both ≤ b.
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An example of interpolation:

1) IN.....VERTED

2) INTROVERTED


An example of extrapolation:

1) .......PL.......

2) :confused:


Exohumanism is an udesirable, inverted and perverted inclination to maliciously alter the future -- and the past.
 
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epix said:
There is no fractal extrapolation, and if there is, show me one.
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The place value method is a fractal where interpolation is used at the right side of the decimal point (for example: 0.1, 0.01, 0.001 , ...), and extrapolation is used at the left side of the decimal point (for example: 1.0, 10.0, 100.0, ...).

For example:

place_value_chart-3.gif
( http://www.mathatube.com/place-value-home.html )

epix said:
Lines are made of points with dim=0.
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1() is not a collection of any amount of 0().
 
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epix said:
An example of interpolation:

1) IN.....VERTED

2) INTROVERTED


An example of extrapolation:

1) .......PL.......

2) :confused:


Exohumanism is an udesirable, inverted and perverted inclination to maliciously alter the future -- and the past.
Click to expand...

You are using 0(a) ≤ 0(x) ≤ 0(b) by ignoring the fact that you actually using 1(0(a) ≤ 0(x) ≤ 0(b)), such that no 0() is both ≤ to another 0(), and only 1() can be both ≤ w.r.t any given pair of different 0(), for example: 1(0(a) ≤ 0(x)).

EDIT:

Since the real-line is 1(), then no collection (ordered or
unordered) of 0() can reach its level of existence.

In this case we clearly distinguish between local numbers and non-local
numbers, for example: π is a local number that has an exact location along
1(), but since 1() is non-local w.rt any given amount of 0(), then 3.14…[base
10] is a non-local number that its exact location along 1() does not
exist. This example can be extended to any given irrational number.

Non-local numbers are not representations of local numbers
but each one of them is a unique path along a non-finite fractal,
which its exact location along 1() does not exist.
 
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doronshadmi said:
The place value method is a fractal where interpolation is used at the right side of the decimal point (for example: 0.1, 0.01, 0.001 , ...), and extrapolation is used at the left side of the decimal point (for example: 1.0, 10.0, 100.0, ...).

For example:

[qimg]http://www.mathatube.com/images/place_value_chart-3.gif[/qimg] ( http://www.mathatube.com/place-value-home.html )
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Where is the pic of that fractal?


1() is not a collection of any amount of 0().
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You just saw that there is no way to distinguish a line from a collection of points. You can say that it isn't so, but you cannot prove it outside the domain of Doronetics, which can't be understood by anyone but you.

The only conceivable argument would concern the Koch form: when the number of iterations approaches infinity, the form is a collection of line segments and points whose number approaches infinity as well. That means the Koch curve cannot be covered by points alone. The problem is that if a line segment cannot be fully covered by points, there is a sub-segment where vertex/inflection points don't exist, and if they don't, there is no Koch curve, coz you can't "bend" a line without the point of inflection being present. The reason why the Koch curve can exist is that the initial line (0-iteration) is a collection of points whose number approaches infinity. Two of them are the end points and the rest are the infection points.
Have a nice bending.
 
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doronshadmi said:
You are using 0(a) ≤ 0(x) ≤ 0(b) by ignoring the fact that you actually using 1(0(a) ≤ 0(x) ≤ 0(b)), such that no 0() is both ≤ to another 0(), and only 1() can be both ≤ w.r.t any given pair of different 0(), for example: 1(0(a) ≤ 0(x)).
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I see that the whole world of mathematics is about to collapse, unless the math folks stop ignoring the facts laid down by Doronetics.
The work of misguided pagans available for perusal here: http://en.wikipedia.org/wiki/Interval_(mathematics)
 
epix said:
The reason why the Koch curve can exist is that the initial line (0-iteration) is a collection of points whose number approaches infinity. Two of them are the end points and the rest are the infection points.
Have a nice bending.
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Exactly the opposite.

No amount of 0() along 1() changes the size of the complex 1(0(x) < 0(y)),
no matter how many 0() are between 0(x) and 0(y), exactly because no amount of 0() is 1().
 
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doronshadmi said:
n = 1 to ∞

Saying it over and over doesn't make it true, The Man. The fact remains that in real Mathematics points are not completely cover a line, simply because no amount of 0 to n-1 dimensional spaces is n dimensional space ad infinitum ... exactly because any given dimensional space is not a collection of the previous dimensional spaces.
Click to expand...


Once again, indentify the locations on a line you think is not covered by points.

Your failure to do so “over and over” again simply shows your claim of any “real Mathematics” to simply be false.

doronshadmi said:
The irreducibility of a given dimensional space > 0 to the previous dimensional spaces is exactly the considered energy, and it clealy seen by cases like http://arxiv.org/PS_cache/arxiv/pdf/0910/0910.2709v1.pdf .
Click to expand...

Ok so “energy” is yet another word that you evidently simply don’t understand.



doronshadmi said:
In addition to post http://www.internationalskeptics.com/forums/showpost.php?p=6419092&postcount=11922 , you are invited to look at Dr. Reva Kay Williams' work (University of Florida) which developed a rigorous proof that validated Penrose's mechanism ( http://en.wikipedia.org/wiki/Gravitomagnetism#cite_note-2 ).

Here is a paper of her ( http://arxiv.org/PS_cache/astro-ph/pdf/0210/0210139v4.pdf ) with the title "NEW ENERGY SOURCE CONTROLLED BY GRAVITY ALONE?" ( the published version is in http://iopscience.iop.org/0004-637X/611/2/952/ ).
Click to expand...


In addition to this post where you are again asked above to show any locations on a line that you think are not or can not be covered by points, you are also invited to show that you understand any of those papers you cited as well as how and why you think (specifically based on the papers themselves) they are relevant to your OM nonsense.
 
doronshadmi said:
Exactly the opposite.

No amount of 0() along 1() changes the size of the complex 1(0(x) < 0(y)),
no matter how many 0() are between 0(x) and 0(y), exactly because no amount of 0() is 1().
Click to expand...

If you think it's the other way around, why do you endorsing what is said?

Originally Posted by epix
The reason why the Koch curve can exist is that the initial line (0-iteration) is a collection of points whose number approaches infinity. Two of them are the end points and the rest are the infection points.
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Is there a spot in the circumference of the circle for which a point doesn't exist, meaning the spot cannot be located. YES or NO?
 
epix said:
Is there a spot in the circumference of the circle for which a point doesn't exist, meaning the spot cannot be located. YES or NO?
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1) A circumference of a given circle exists even if there is not even a single 0() along it.

2) If there are 0() along a circumference of a given circle, each one of them is different than any other 0(), no matter how many scale levels are researched.

In other words, 0(x)≠0(y) is an invariant fact, where ≠ is an uncovered domain that is both a differentiation (enables 0(x),0(y) distinction) and an integration (enables the existence of 0(x),0(y) as a pair).
 
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The Man said:
Once again, indentify the locations on a line you think is not covered by points.
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0(x)≠0(y) is invariant upon infinitely many scale levels, where ≠ is an uncovered domain that is both a differentiation (enables 0(x),0(y) distinction) and an integration (enables the existence of 0(x),0(y) as a pair).

In other words, Traditional Math can't comprehend 1(0(x)≠0(y)).

The Man said:
Ok so “energy” is yet another word that you evidently simply don’t understand.
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The irreducibility of a given dimensional space > 0 to the previous dimensional spaces is exactly the considered energy, which your false model of collection of only 0() evidently can't comprehend.
 
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doronshadmi said:
1) A circumference of a given circle exists even if there is not even a single 0() along it.
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You can axiomize the heck out of Virgin Mary and declare anything you want, but you can't make that self-evident. You can stand on the pulpit and hold your sermon 24/7 and it's still no-go, coz there is a requirement for statements of this nature called "acceptance." Even God had to utter something like "let there be light" to make things happen. Your circle appears by itself and its size cannot be determined, coz there are no points of intersection on its circumference and therefore you can't measure its diameter. See, the end points of the diameter line must share the same location with two opposite points on the circumference in order to measure the diameter. So you can't define that phantom circle, and as such, the circle is useless for anything except the halo over the saints.
 
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doronshadmi said:
0(x)≠0(y) is invariant upon infinitely many scale levels, where ≠ is an uncovered domain that is both a differentiation (enables 0(x),0(y) distinction) and an integration (enables the existence of 0(x),0(y) as a pair).

In other words, Traditional Math can't comprehend 1(0(x)≠0(y)).
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No Doron it simply demonstrates that you can't comprehend that "≠" is not a location on a line. So you still simply can not show any location or locations on a line that are not or can not be covered by points.

doronshadmi said:
The irreducibility of a given dimensional space > 0 to the previous dimensional spaces is exactly the considered energy, which your false model of collection of only 0() evidently can't comprehend.
Click to expand...

Ok so “energy” is still just another word that you evidently simply don’t understand and “evidently can't comprehend”.
 
The Man said:
No Doron it simply demonstrates that you can't comprehend that "≠" is not a location on a line.
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No The Man it simply demonstrates that you can't comprehend that "≠" is the non-local property of 1() w.r.t 0().

By using Traditional Math, please prove that variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0.
 
DazzaD said:
Really?

So the sum of a geometric series with a common ratio less than 1 does not have a limit?

...
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doronshadmi said:
Please look at S in http://www.internationalskeptics.com/forums/showpost.php?p=6400287&postcount=11858.

Its does not have a sum if the series 2(a+b+c+d+...) is infinite.
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He didn't say 'sum', he said 'limit', which is what you originally said.


ETA: Ah, I see it was yet another example of your ninja editing skills; you've been told about the dishonesty of that before.
 
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doronshadmi said:
epix, Pointless_topology is also under Non-locality\Locality Linkage, because whenever multiplicity is used, there is Non-locality among the considered elements. so?
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A very apt description, as I'm sure has been noted before. "Pointless" is exactly the word to describe OM.
 
epix said:
Your circle appears by itself and its size cannot be determined,
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We do not need to know the size of a given circle, in order to know that it is 1().

In order to know the size of a given circle, the complexity 1(0()) is used.
 
doronshadmi said:
http://www.internationalskeptics.com/forums/showpost.php?p=6422678&postcount=11927
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Collection is a process, not an amount. You made it synonym to plural. You collect data and if you manage to get only one, then you still collected data.
Altering the meaning of words to suit your needs will not sit well with your attempt to reorganize math.

Let's practice extrapolation: 1, 2, 3, 9, 24, 76, 236, ...

Where does it go? These numbers are you invention, remember?
 
doronshadmi said:
We do not need to know the size of a given circle, in order to know that it is 1().
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We don't draw a circle to know its dimensionality; there are much more useful things you can do with circles. The dimensionality of a circle is not important and is rarely mentioned. For example the article in Wiki doesn't mention the dimensionality of the circle not even once.
http://en.wikipedia.org/wiki/Circle

You are swimming in the Sea of Irrelevance and the time is getting short.
 
The Man said:
In addition to this post where you are again asked above to show any locations on a line that you think are not or can not be covered by points, you are also invited to show that you understand any of those papers you cited as well as how and why you think (specifically based on the papers themselves) they are relevant to your OM nonsense.
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The function f(x)=1/x on the real line has a singularity at x = 0, where it seems to "explode" to ±∞ and is not defined.
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( see http://en.wikipedia.org/wiki/Mathematical_singularities ).

By understanding 1/0 as 1()/0() we actually discover the irreducibility of 1() to 0(), such that 1(0()) where, 1() is non-local w.r.t 0() and 0() is local w.r.t 1().

In other words, the "explosion" to ±∞ is actually the irreducibility of 1() to 0(), such that no amount of 0() is 1().

n=1 to ∞

k= 0 to n-1

The irreducibility of n() to k() stands at the basis of gravitational singularity ( http://en.wikipedia.org/wiki/Gravitational_singularity ).
 
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doronshadmi said:
In other words, the "explosion" to ±∞ is actually the irreducibility of 1() to 0(), such that no amount of 0() is 1().
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The irreducibility of 1() to 0() means that there can't be 1/2() or 1/3()... In other words there can't be no values between 1 and 0 that would lead to the reduction of 1 toward 0. But that's not so, as I already told you once:

In mathematics, the Hausdorff dimension (also known as the Hausdorff–Besicovitch dimension) is an extended non-negative real number associated with any metric space. The Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional vector space equals n. This means, for example the Hausdorff dimension of a point is zero, the Hausdorff dimension of a line is one, and the Hausdorff dimension of the plane is two. There are however many irregular sets that have noninteger Hausdorff dimension.
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"Noninteger" means a fraction, such as 1/2, 1/3, 1/4... and therefore 1() is reducible. But it cannot be reduced all the way to 0() through reduction by division, the same way 0() can't be expanded to 1() through multiplication.

If you are in the Euclidean space, then be advised that

Many constructs within Euclidean geometry consist of an infinite collection of points that conform to certain axioms. This is usually represented by a set of points; As an example, a line is an infinite set of points of the form

(see formula)

where (parameter) through (parameter) and (parameter) are constants and 'n' is the dimension of the space. Similar constructions exist that define the plane, line segment and other related concepts.
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http://en.wikipedia.org/wiki/Point_(geometry)

If your are not in Euclidean space, where are you then?

Once a 1-D object is defined continuous, then its definition assures that there is no point on the object that cannot be located. f(x) = 1/x or g(x) = Log(x) are not defined continuous in the domain -∞ < x < ∞. If this is what you mean by "not all points can cover 1()," then you just made a "far-reaching discovery."
 
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